I sometimes hear about game designers who are just naturally mathematically gifted. Not being one of those designers, I am fortunate to have Mark Sherry as a contact.

Here's our process. I'll tweet a random game idea or mention it on the blog, without really considering the long-term mathematical implications. That's where Mark's giant brain steps in, working out every idiosyncratic permutation of every variable. At times, he'll even create simple AI players, each with different strategies, just to see how those players stack up against each other.

He shares his observations and I'll be confused for many hours until he dumbs it down enough for me. Eventually I sorta "get" it and I'll get back to work tweaking rules if necessary. Here's an example of Mark in action, analyzing Split Decision.

We know from these charts that if a player chooses the highest pair at all times, he's probably going to get a 10. Working from that base, you can adjust the thematic and fictional elements of your game to center around that number. Make that number tempting enough that a player would want it, despite whatever long-term costs might bear out in the future.

Sometimes Mark will send something like this:

In something like the Matrix game, the goal is presumably to last as long as possible, while succeeding in tasks as much as possible. There is an optimal strategy for that, and I believe I've found it. To do something like choose always red is suicidal - you'll last only 5 turns. Playing smart, you'll last closer to 10 turns. (Average: 28 dice rolls for a 3 player game.)

And that gets translated into some simple game rules like this:

Rules: Play goes around the circle. Each player has his or her own red and blue tracks. If a player's track hits 10 items, then they are eliminated. The target number is 7. If a player fails to reach the TN twice, they are eliminated. Play continues until all players are eliminated. (Unimplemented variant(s): If a player is eliminated, all other players can either remove a dot from a track, or cancel a failure) With three players and 10000 games, the average game length was 28.721 dice rolls long.

Which leads to conclusions like this:

The maximum game length is 10 turns per player, since after that point, you've accumulated 20 track points. Given the greatest number of track points you can have before being eliminated is 9+9=18, you have to have completed at least one of the tracks.That gives you a frame for your game. With an endpoint in sight, you can create a pacing mechanic that works within those boundaries.

Needless to say, I recommend getting Mark's input if you need some alpha testing for your game. In my mind, it's as important as getting a good editor.